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Saturday, 31 October

JEE Main · Maths · Limits and Derivatives

Conjugation vs L'Hopital for Radicals

JEE Main asked Conjugation vs L'Hopital for Radicals 4 times in 4 of the 108 shifts Lumi analysed, in 2021, 2022 and 2024. It belongs to L'Hopital's Rule, in Limits and Derivatives (Maths). The longest wait between two years asking it was 2 years. In 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
3 of 8
First asked
2021
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200.03’210.04’220’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20242 of 18
  • 20230 of 12
  • 20221 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: calculation.

  • Evaluate limits with nested radicals
  • Limit of ratio of fractional powers

Difficulty

Easy 0Medium 2Hard 2

1 of the 4 questions had a numerical answer.

Every question

All 4 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 27 Jan 2024, Shift 1 · Q9If a=lim⁡x→01+1+x4−2x4a=\lim_{x\to0}\dfrac{\sqrt{1+\sqrt{1+x^4}}-\sqrt{2}}{x^4} and b=lim⁡x→0sin⁡2x2−1+cos⁡xb=\lim_{x\to0}\dfrac{\sin^2 x}{\sqrt{2}-\sqrt{1+\cos x}}, then the…MediumSingle correct
  2. 4 Apr 2024, Shift 1 · Q24If lim⁡x→1(5x+1)1/3−(x+5)1/3(2x+3)1/2−(x+4)1/2=m5n(2n)2/3\lim_{x\to1}\frac{(5x+1)^{1/3}-(x+5)^{1/3}}{(2x+3)^{1/2}-(x+4)^{1/2}}=\frac{m\sqrt{5}}{n(2n)^{2/3}}, where gcd⁡(m,n)=1\gcd(m, n)=1, then…HardNumerical value
  3. 25 Jun 2022, Shift 2 · Q5…HardSingle correct
  4. 27 Aug 2021, Shift 2 · Q66If lim⁡x→∞(x2−x+1−ax)=b\lim_{x \to \infty} \left(\sqrt{x^2 - x + 1} - ax\right) = b, then the ordered pair (a, b) is :MediumSingle correct

Shifts: 27 Aug 2021, Shift 2, 25 Jun 2022, Shift 2, 27 Jan 2024, Shift 1, 4 Apr 2024, Shift 1.

Same topic

Other ideas in L'Hopital's Rule

L'Hopital's Rule has 18 ideas JEE Main has asked; 9 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas